An Introduction to Density

How Much Stuff Makes Up Different Stuff?

Density is mass per unit volume. A material of low density will float on one of higher density. Dorling Kindersley / Getty Images

A material's density is defined as its mass per unit volume. It is, essentially, a measurement of how tightly matter is crammed together. The principle of density was discovered by the Greek scientist Archimedes.

To calculate the density (usually represented by the Greek letter "ρ") of an object, take the mass (m) and divide by the volume (v):

ρ = m / v

The SI unit of density is kilogram per cubic meter (kg/m3).

It is also frequently represented in the cgs unit of grams per cubic centimeter (g/cm3).

Using Density

One of the most common uses of density is in how different materials interact when mixed together. Wood floats in water because it has a lower density, while an anchor sinks because the metal has a higher density. Helium balloons float because the density of the helium is lower than the density of the air.

When your automotive service station tests various liquids, like transmission fluid, they will pour some into a hydrometer. The hydrometer has several calibrated objects, some of which float in the liquid. By observing which of the objects float, it can be determined what the density of the liquid is ... and, in the case of the transmission fluid, this reveals whether it needs replacing yet or not. 

Density allows you to solve for mass and volume, if given the other quantity. Since the density of common substances is known, this calculation is fairly straightforward, in the form:

v * ρ = m
m / ρ = v

The change in density can also be useful in analyzing some situations, such as whenever a chemical conversion is taking place and energy is being released. The charge in a storage battery, for example, is an acidic solution. As the battery discharges electricity, the acid combines with lead in the battery to form a new chemical, which results in a decrease in the density of the solution.

This density can be measured to determine the battery's level of remaining charge.

Density is a key concept in analyzing how materials interact in fluid mechanics, weather, geology, material sciences, engineering, and other fields of physics.

Specific Gravity

A concept related to density is the specific gravity (or, even more appropriate, relative density) of a material, which is the ratio of the material's density to the density of water. An object with a specific gravity less than 1 will float in water, while a specific gravity greater than 1 means it will sink. It is this which allows, for example, a balloon filled with hot air to float in relation to the rest of the air.

Edited by Anne Marie Helmenstine, Ph.D.